Related papers: The Curie-Weiss model with complex temperature: ph…
The object of this study is a cell model with Curie-Weiss interaction potential. We have already proved the possibility of a mathematically rigorous transition from a continuous system of interacting particles to such a model and made an…
The Curie-Weiss model is an exactly soluble model of ferromagnetism that allows one to study in detail the thermodynamic functions, in particular their properties in the neighbourhood of the critical temperature. In this model every…
This contribution is devoted to cover some technical aspects related to the use of the recently proposed energy probability distribution zeros in the study of phase transitions. This method is based on the partial knowledge of the partition…
A single-sort continuum Curie-Weiss system of interacting particles is studied. The particles are placed in the space $\mathbb{R}^d$ divided into congruent cubic cells. For a region $V\subset \mathbb{R}^d$ consisting of $N\in \mathbb{N}$…
Phase transitions are typically accompanied by non-analytic behaviors of the free energy, which can be explained by considering the zeros of the partition function in the complex plane of the control parameter and their approach to the…
An analog of the continuum Widom-Rowlinson model is introduced and studied. Its two-component version is a gas of point particles of types 0 and 1 placed in $\mathds{R}^d$, in which like particles do not interact and unlike particles…
We investigate the convergence properties of finite-temperature perturbation theory by considering the mathematical structure of thermodynamic potentials using complex analysis. We discover that zeros of the partition function lead to poles…
This paper studies a generalization of the Curie-Weiss model (the Ising model on a complete graph) to quantum mechanics. Using a natural probabilistic representation of this model, we give a complete picture of the phase diagram of the…
We propose a relationship between thermodynamic phase transitions and ground-state quantum phase transitions in systems with variable Hamiltonian parameters. It is based on a link between zeros of the canonical partition function at complex…
We discuss a numerical analysis employing the density of partition function zeroes which permits effective distinction between phase transitions of first and second order, elucidates crossover between such phase transitions and gives a new…
Adding activity or driving to a thermal system may modify its phase diagram and response functions. We study that effect for a Curie-Weiss model where the thermal bath switches rapidly between two temperatures. The critical temperature…
We review the non-zero temperature relaxational dynamics of quantum systems near a zero temperature, second-order phase transition. We begin with the quantum Ising chain, for which universal and exact results for the relaxation rates can be…
We construct the exact partition function of the Potts model on a complete graph subject to external fields with linear and nematic type couplings. The partition function is obtained as a solution to a linear diffusion equation and the free…
Interacting quantum systems illustrate complex phenomena including phase transitions to novel ordered phases. The universal nature of critical phenomena reduces their description to determining only the transition temperature and the…
The large N limit of the Gross-Neveu model is here studied on manifolds with constant curvature, at zero and finite temperature. Using the zeta-function regularization, the phase structure is investigated for arbitrary values of the…
The zeros of the partition function of the ferromagnetic q-state Potts model with long-range interactions in the complex-q plane are studied in the mean-field case, while preliminary numerical results are reported for the finite 1d chains…
At low temperature a thermodynamic system undergoes a phase transition when a physical parameter passes through a singularity point of the free energy, corresponding to formation of a new order. At high temperature the thermal fluctuations…
We study the Roberge-Weiss phase transition numerically. The phase transition is associated with the discontinuities in the quark-number density at specific values of imaginary quark chemical potential. We parameterize the quark number…
The equation of state of a system at equilibrium may be derived from the canonical or the grand canonical partition function. The former is a function of temperature T, while the latter also depends on the chemical potential \mu for…
A recently developed technique for the determination of the density of partition function zeroes using data coming from finite-size systems is extended to deal with cases where the zeroes are not restricted to a curve in the complex plane…